Future generations writing the history of climate change may be struck by an apparent paradox: while millions of educated people – perhaps most of them – alive in the first decade of the 21st century acknowledged the threat posed by the buildup of greenhouse gasses and their part in creating it, only a tiny number did anything about it. Poll after poll underlines this disconnect; one extensive survey carried out by the Department for Transport last year found that 81% of adults were very or fairly concerned about climate change and three quarters said they were willing to change their behaviour to help combat it. But go looking for examples of that changed behaviour beyond putting out the recycling and you're likely to be disappointed. With the exception of a small, saintly portion of the population, our response to global warming is a classic case of all mouth and trousers.

And seen from this end of the century it's not hard to see why. Even if most of us appreciate, as my colleague Leo Hickman describes it, that sawing away at the branch we are sitting on can't be a good idea, actually doing something about it requires us both to execute a leap of imagination and to stretch our ideas of self-interest and moral responsibility. We are asked to make real sacrifices now to protect future generations from a risk, the precise nature of which is still uncertain. Homo sapiens has never been terribly good at this kind of long-term thinking – some evolutionary biologists suggest the very wiring of our brains conspires against it – and the rise of liberal individualism has made it harder, if anything, to forge collective responses to problems that do not threaten our short-term self-interest.

Then there is the awkward reality, often glossed over by the those seeking to promote action on climate change, that the children and grandchildren of those of us in the rich north will not be among those worst hit by the effects of warming. In fact, how many Britons do not hear talk of a two- or three-degree increase in average temperatures and secretly wonder if a climate more like Seville than Stockholm might be rather pleasant?

Even those well-intentioned enough to want to do their bit, can quickly find themselves feeling powerless and paralysed in the face of an issue of this scale. What's the point of acting individually to reduce your emissions if most other people carry on just as they are? In fact what's the point of doing anything in Britain when it accounts for just 2% of world emissions? What about that new coal-fired power station the Chinese are building every week? Doesn't it make a mockery of anything I, or even Britain, might do?

Climate change is perhaps the most extreme example of what the American ecologist Garrett Hardin called a tragedy of the commons. Hardin considered the example of herders raising cattle on a shared field. It was in each herder's narrow interest to keep adding more cows, since each enjoyed all the benefits of an extra cow, while the effects of the extra cow on the pasture were shared by all. And so the herders moved ineluctably towards disaster.

At the same time, much of the discourse about climate change does little to convey a sense of urgency. Scientists and politicians talk about "stabilising" carbon dioxide levels some time later this century. Diplomats wrangle over targets for 2020 and 2050. It all sounds like something we can afford to put off worrying about until next month or next year. The penny that has not yet dropped with most of us is that we have arrived at a make-or-break moment: if we are to have any real chance of avoiding dangerous warming, the scientists now agree, global emissions must peak within the next five to 10 years and then begin to fall. And if we are to have any chance of achieving that goal, we need to start cutting now. Tomorrow, next week, next month.

The environmental thinker Tim Helweg-Larsen explains the urgency by likening climate change to a bath with the tap running. Since warming is caused by the total amount of greenhouse gases in the atmosphere, it is the volume of water in the bath, rather than simply how much water is flowing into it, that we must worry about. If the bath is close to overflowing and we are still running water into it quicker than it can flow out of the plughole, we need to begin closing the taps immediately, or our chances of stopping it overflowing will be far slimmer.

A gathering of some of the world's most eminent scientists in London in May was quite precise about how quickly we must begin turning the taps: unless world carbon emissions begin falling within just six years, they concluded, we have little chance of avoiding warming beyond the critical level of two degrees. Above that level, scientists fear so-called "feedbacks" could kick in, leading to runaway warming and extreme weather events such as droughts and floods that would leave millions homeless and starving.

The 10:10 campaign, which is launched today in partnership with the Guardian, is designed both to answer the call for immediate action, and to offer individuals and organisations a meaningful way of taking it. It is the brainchild of Franny Armstrong, the irrepressible film-maker behind The Age of Stupid, a powerful docudrama about our failure to tackle climate change. The idea is compellingly simple: by signing up, individuals and organisations from multinational companies to schools and hospitals commit to doing their best to cut their emissions by 10% by the end of 2010, precisely the sort of deep, quick cut the scientists say is needed.

A modest challenge

Central to the 10:10 campaign is an acknowledgement that the kind of action we are typically urged to take to combat climate change is all too often either footling or forbiddingly hair-shirted. As the environmental writer George Marshall has powerfully argued, focusing on easy, "achievable" targets such as recycling has both distorted public understanding of the impacts of our lifestyle and risks trivialising the issue. At the same time the kind of scorched-earth lifestyle transformation some environmentalists demand is more than most of us are willing to embrace. At least yet. "You are being asked not only to change your life but to make your life very different to the people around you," says the low-carbon expert Chris Goodall. "It's almost an aggressive act. All of a sudden you move outside the mainstream milieu."

At the risk of evoking Blair's third way, 10:10 aims to find a space between these poles by promoting action that is both achievable and meaningful. While collectively cutting 10% of emissions in the next year or so would represent a significant step on the road to a low carbon Britain, it is for each of us – and for most businesses – a relatively modest challenge. The first 10% is what the experts call the low-hanging fruit, the savings we can make through relatively small sacrifices such as changing lightbulbs, insulating our homes more effectively, turning down our central heating or swapping one or two flights a year for rail journeys. Even for those of us who have already taken these easy steps, the next 10%, as some of our case studies show, is within reach without wholesale renunciation of a western consumer lifestyle. A group of Oxford householders who recently embarked on a carbon diet managed to reduce their emissions by between 25% and 30% during the course of the last year.

Over the next 16 months we'll be offering plenty of advice on how to do it and following the progress of a number of families, businesses and other organisations as they try to hit the 10% target. We'll also create space online and in print for you to swap your own know-how, experiences and support. The emphasis will be on properly quantifying the changes you can make so you can decide what is meaningful and what is simply symbolic.

The campaign has already created a remarkable degree of buzz and excitement. Even before it is formally launched today, it has attracted a diverse and formidable legion of supporters ranging from the online grocer Ocado, three major energy companies, a Premiership football club, unions and NGOs to influential figures in the arts, showbusiness, religion, TV and politics.

One measure of the power of its central idea is the improbable alliances it has forged. CEOs of energy companies find themselves in bed with activists who a few months ago might have been chained to the fences outside their power stations. The Women's Institute marches to the rhythm of painfully cool indie bands Stornoway and Reverend and the Makers (who will play for free at this evening's launch event at Tate Modern).

A moral obligation

Over the next few months, the 10:10 team hope tens – perhaps hundreds – of thousands more will don a 10:10 tag made from scrap metal salvaged from retired aircraft. (The hurried manufacture of large numbers of these over the summer produced one of the campaign's moments of black comedy when a rumour began circulating that they were tags which would be used to label the thousands of fatalities the government was expecting to be caused by swine flu.) The 10:10 team have no intention of stopping there; once they have amassed a significant number of pledges from individuals, companies and institutions, they plan to challenge the government to match their commitment.

Though the British government has recently taken some significant steps towards decarbonising the economy, the fact that we find ourselves in need of something close to a miracle to avert disaster reflects a profound failure of leadership by the political classes of all the world's major nations. Most governments and their electorates have been locked in a disastrous standoff, neither willing to take action till the other shows they are serious about the problem. 10:10 is partly about breaking that destructive impasse.

Sceptics will retort with the usual questions: why take any form of unilateral action when we are months away from what has been billed as a critical international climate conference? How can any campaign in marginal little Britain have an impact on the ultimate global problem?

Reflecting the pluralism of the 10:10 coalition, different answers emerge from different corners of the campaign. Talk to Goodall and he will answer unashamedly in terms of simple moral responsibility: "If there is a problem that has been caused by us and is being caused by us then we have a moral obligation to do something about it. As individuals we have to live our lives as we want other people to live their lives." The trouble, Goodall reflects a little sadly, is that the rise of aggressive materialism has made such a categorical position look quaint, if not outright lampoonable.

Ideas have power

Armstrong has a more pragmatic view of the role 10:10 could play in bringing about significant global action. Few who know anything about it believe the best deal on the cards in Copenhagen, the key conference in December at which world leaders will attempt to hammer out a global climate change treaty, is anything like tough enough to avert dangerous warming. Armstrong believes forcing the British government to move faster could put it in a leadership position that would enable it to push for a tougher deal. It is an optimistic but not completely far-fetched vision. Developing nations – in particular China and India – have consistently argued that they won't submit to binding carbon limits until they see real evidence of the rich world tackling the problem it substantially created. I have heard Chinese diplomats talk about the importance of seeing meaningful action from Britain and Europe. Helweg-Larsen talks compellingly about the value of taking an inspirational lead: "We have to demonstrate progress and we have to be inspiring each other with action. Ideas have power."

More radical critics will argue that 10:10 is just "feelgood" window dressing designed to paper over the cracks in a broken economic model. Even the moving spirits of the campaign would not claim it was more than a useful first step towards the deeper transformation of our lifestyles that will be required. But it is significant that some of the most exacting experts in the field have endorsed the campaign as being in line with what the science demands – figures such as outspoken British climatologist Kevin Anderson who has criticised both politicians and his colleagues for failing to be honest about the perilousness of our position.

A while ago I had a dispiriting conversation with another eminent European scientist. He is a natural optimist but sounded unusually low. He had recently been asked to brief a leading European political figure on the latest scientific understanding of climate change. The leader listened then described the best deal he believed possible at Copenhagen: a 50% global cut in emissions against 2000 levels – by 2050. The scientist explained that such a deal would give us only a 50% chance of avoiding a temperature rise above the critical two-degree level that experts believe could trigger runaway warming, but the politician insisted that a tougher deal would never get off the drawing board. "I asked, who would fly on an airline that had a 50:50 chance of crashing?" the scientist told me.

10:10 is about declaring that we do not accept those odds. It is about grabbing the wheel from the bus driver who is steering us directly towards an oncoming juggernaut. It is about old-fashioned ideas of responsibility, but also about a more enlightened understanding of our collective self-interest. It is about an optimistic view of what ordinary people can achieve, and of human nature itself. Now over to you.